solve the inequality using an appropriate property of the absolute value. Provide an exact answer using interval notation?

Any help would be appreciated!

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3 Answers

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  • ted s
    Lv 7
    1 month ago

    2 false "answers" because of carelessness....you have 5 < 7 | x/8 - 3 |...multiply everything by ' 8 '......40 < 7 | x - 24 | these all all reals which are (40/7) units away from  24.........( - ∞ , 24 - 40/7) U ( 24 + 40/7 , ∞)....so you should look at the other 2 and find the careless errors...it will help you later on when doing problems

  • Bryce
    Lv 7
    1 month ago

    -7|(1/8)x - 3| + 9< 4

    -7|(1/8)x - 3|< -5

    |(1/8)x - 3|> 5/7

    -5/7>(1/8)x - 3>5/7

    16/7>(1/8)x>26/7

    128/7>x>208/7

  • 1 month ago

    First simplify equation

    -7 * abs(X/8 - 3) + 9 < 4

    -7 * abs(X/8 - 3) < -5

    abs( X/8 - 3) > 5/7  (must flip inequality when dividing or multiplying by negative)

    Then abs means that amount can be positive or negative so

    1) X/8 - 3 > 5/7  and

    2) -(X/8 - 3) > 5/7

    2) becomes X/8 - 3 < -5/7

    so -5/7 < X/8 - 3 < 5/7

    and

     -5 < X * 7/8 - 21 < 5  add 21 to all parts

    16 < X * 7/8 < 26  multiply by 8/7 

    16 * 8 / 7 < X < 26 * 8 / 7

    Is this enough?

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